When it is silent

The LED first

The LED is wired from VCC to the transistor, beside the buzzer, so it lights exactly when the transistor conducts. That makes it a test of everything up to the buzzer: power, ground, the SIGNAL wire, the pin number and the sketch. It says nothing about the buzzer itself.

• Dark while the sketch should be playing: nothing reaches the transistor. Wiring or pin number.
• A dim glow during notes: the transistor is switching. If there is still no sound, look at the buzzer: something pressed against its side port, or a damaged part.
• Fully lit, steady: SIGNAL is HIGH and staying there. No sound, and about 200 mA through the coil. Fix the sketch before anything else.

Stuck HIGH is the one to fix at once

Every other fault here is harmless: silence, a quiet note, a stopped PWM pin. A stuck HIGH is not silent in the way that matters. The coil has only its 16 Ω to limit it, so from 3V3 it draws about 200 mA and from 5V about 300 mA, two or three times what the buzzer takes while playing, for as long as the pin stays HIGH. Those figures are worked out from the datasheet, not measured, and the buzzer is rated for a square wave, not a steady current.

It usually comes from a sketch written for an active buzzer, which switches its input HIGH for sound, or from a duty of 255. Passive means you make the wave explains why the same sketch fails here.

Pitch before volume

A note that is too quiet is usually a note that is too low. The datasheet's curve rises by about 20 dB from middle C to 2.7 kHz. Pitch, and where it is loudest has the curve; move the tune up before reaching for VCC or the duty.